MoS2: a Choice Substrate for Accessing and Tuning the Electronic

Properties of Graphene

Chih-Pin Lu1,2

, Guohong Li1, Li-Min Wang

2, K. Watanabe

3, T. Taniguchi

3 and Eva Y.

Andrei1

1 Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey

08855, USA

2 Department of Physics, National Taiwan University, Taipei 10617, Taiwan

3National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044,

Japan

Research into the electronic properties of graphene and its viability for device

applications has fueled an ongoing quest for substrate materials that are minimally

invasive. While graphite was found to be perfectly suited for shielding graphene from

external perturbations, its metallic screening precludes control of the carrier density

by gating, which renders it unsuitable for device applications. Another candidate,

hBN, which is atomically flat, chemically inert, and allows gating, can cause

significant bandstructure reconstruction in graphene due to the close match of their

atomic structures. Here we report on the suitability of MoS2 substrates as measured by

scanning tunneling microscopy and Landau level spectroscopy in a device

configuration which allows tuning the carrier density of graphene by gating. We find

that, similarly to hBN, graphene on MoS2 is ultra-flat producing long mean free paths

and sharp Landau levels down to magnetic fields of 2T, while completely avoiding

the band structure reconstruction caused by hBN. Importantly, we find that the

screening properties of the MoS2 substrate can be tuned with relatively low gate

voltages from insulating to metallic leading to a substantial increase in the scattering

length. The use of MoS2 substrates thus provides unique opportunities to access the

intrinsic electronic properties of graphene and to study in situ the effects of screening

on electron-electron interactions and transport.

The vulnerability of atomically thin layers such as graphene1-3

to environmental

disturbances has prompted an ongoing search for substrates that can support the

material without perturbing its electronic structure. Graphite substrates were found to

be by far the least invasive, making it possible to observe the intrinsic low energy

spectrum of graphene by using scanning tunneling microscopy (STM), spectroscopy

(STS)4-7

, and cyclotron resonance (CR)8 measurements. Landau level spectroscopy

showed that on graphite substrates the quasiparticle lifetime in graphene is intrinsic,

originating from electron-electron interactions, with the only source of external

scattering being the sample boundaries5. In this sense graphite substrates are ideally

suited for accessing the low energy spectrum of graphene. However the strong

metallic screening of bulk graphite, which precludes control of the carrier density by

gating and masks the electron-electron interactions, imposes severe limitations for

both applications and fundamental studies. The alternative is to use insulating

substrates, but the versatility gained comes at the price of enhanced sensitivity to

surface corrugations 9-11

and impurities12-16

, which create electron-hole puddles that

obscure the low energy electronic properties at the Dirac point17

. These perturbations

can be mitigated by the use of atomically flat18

and chemically inert substrates such as

hexagonal boron nitride (hBN)19-22

. However the close match between the lattice

structure of graphene and the substrate leads to a spatial modulation which

significantly perturbs the electronic spectrum by producing Van-Hove singularities23,

24, band gaps

25 and new sets of Dirac cones

26-30. Here we show that atomically flat

MoS2 substrates provide access to the intrinsic band structure of graphene while at the

same time allow tuning via a gate voltage both the carrier density and the strength of

screening.

MoS2 is a semiconductor in the layered transition metal dichalcogenite family

consisting of covalently bonded S-Mo-S sheets held together by the van der Waals

force. Its weak interlayer coupling facilitates the extraction of ultra-thin layers by

exfoliation. Bulk MoS2 has an indirect bandgap of 1.2~1.3eV31

which, due to

quantum confinement, crosses over to a direct bandgap of ~1.9eV when the material

is exfoliated down to a monolayer32

. Thin layers of MoS2 are well suited to serve as

the channel material in FET applications, exhibiting high room temperature mobility,

almost ideal switching characteristics, and low standby power dissipation33-36

. The

fact that the position of the Femi energy can be promoted from the gap to the

conduction band with relatively modest gate voltages, allows tuning the screening

properties of MoS2 films from insulating to metallic. Further, the absence of dangling

bonds and of surface states renders its surface inert, clean and minimally invasive.

The large lattice mismatch between MoS2 and graphene, together with its chemical

inertness and the tunable screening, renders MoS2 ideally suited as a substrate

material for studying graphene by STM and STS.

We employed thin MoS2 flakes that were exfoliated from commercial 2H-MoS2

crystals (SPI CAS # 1317-33-5) and deposited onto a 300nm chlorinated SiO2

substrate37

capping a degenerately p-doped Si gate. The flakes were identified by

optical microscopy and their thickness was measured using atomic force microscopy

(AFM) in ambient conditions. Subsequently a flake of graphene which was exfoliated

from bulk HOPG and deposited on a thin PMMA film was optically aligned with the

MoS2 substrate and pressed onto it while heating the sample stage to ~100 oC

19 . We

employed e-beam lithography followed by electron-beam evaporation at a base

pressure of 2×10-7

Torr to prepare the Ti/Au (3nm/70nm) contacts. Similar methods

have been used to prepare samples on hBN substrates. As for grapheme on SiO2,

graphene was deposited directly without the special alignment process. The devices

were baked for 3hrs in forming gas (90% Ar, 10% H2) at 250 oC prior to performing

STM measurements in a home-built STM operating at temperatures down to 4K and

in magnetic fields up to 12T. Coarse X-Y motors were used to locate the micron sized

sample38

. Figure1(a) illustrates the measurement set up and electrode configuration

for the gated STM/STS studies. The images were acquired in constant current mode

with the bias voltage, Vb, applied to the sample and using Pt-Ir tips mechanically cut

from a polycrystalline wire. Differential conductance, dI/dV which is proportional to

the local density of states (LDOS) 39

, was measured with lock-in detection at

frequency f = 440Hz with fixed tip to sample distance. The gate voltage, Vg, was

applied between the Si backgate and the sample. This measurement configuration

which combines STS with gating capabilities makes it possible to study the effect of

screening on the electronic properties of graphene.

Figures 1(b-e) show STM topography images, 80nm × 80nm in size, of graphene

on several substrates: MoS2 (b), SiO2 (c) and hBN (d,e). In Figure 1(f) we compare

the height profile on these substrates taken along the lines indicated in the topography

images. Since graphene tends to conform to the substrate its corrugation on atomically

flat surfaces such as MoS2 or hBN is naturally much smaller than on amorphous

surfaces such SiO2. Indeed we find that the average surface corrugation of graphene

on hBN (0.1nm), as shown in Figure 1(d), is one order of magnitude smaller than on

SiO2 (0.9 nm), consistent with earlier reports9, 20, 21

. This is in marked contrast to the

case shown in Figure 1(e) where in spite of the atomically flat hBN substrate the

surface exhibits a large periodic corrugation with an apparent height of ~0.4nm. The

stark difference between the images in Figures 1(d) and 1(e), both showing the

topography of graphene on hBN, is due to different relative twists between the lattice

orientations of graphene and hBN. The relative twist angle, together with the lattice

mismatch, aBN/a ~ 1.8% between graphene and hBN gives rise to a moire

superstructure of period20

2)cos1)(1(2

)1(a

where aBN and a are the

lattice constants of hBN and graphene respectively. The superstrtucture in Figure 1(e)

is due to the small twist angle, ~0.1o, which gives rise to the large periodic modulation

in topography and in the LDOS. In contrast, the twist angle in Fig. 1(d) is too large

(>20o) to produce a measurable superstructure resulting in the much smoother

appearance. Thus, substrates with lattice structures closely matched to that of

graphene (small ) such as hBN4 or a second layer of graphene

23, can produce a large

disturbance in the band structure, even when they are atomically flat. In contrast, for

substrates with large mismatch such as MoS2 the disturbance is minimal.

Figure 2 shows the evolution of the dI/dV spectra with gate voltage for graphene

deposited on a ~30nm thick MoS2 substrate. All energy measurements are referred to

the Fermi energy (EF), which is the zero of energy. Determining the position of the

DP from the zero field LDOS of graphene on an insulating substrate is a challenging

task7 because the inevitable presence of electron-hole puddles smears out the

minimum at the DP. Furthermore, in the absence of screening the zero-bias anomaly

produces a pronounced minimum which can overshadow the minimum at the DP7, 40

.

The arrows in Fig. 2(a) at the center of the broad minimum are a rough estimate of the

DP position. This choice was guided by the finite field data (Figure 4) where the

position of the DP is much less ambiguous. This is because in a magnetic field the

center of the N=0 Landau level (LL) coincides with the DP and the position of EF

coincides with its zero field value for Vg corresponding to a half filled LL7. Plotting

the gate voltage dependence of ED in Fig.2(b) we find that for Vg < 10V the data

qualitatively follows the massless Dirac fermion spectrum expected for graphene:

√ | |. Here V0 ~ 4.5V represents the voltage to compensate the

unintentional doping, α≈ 6.6 × 1010

cm-2

V-1

is the carrier density per volt of gate

voltage and vF =1.21 2×106 m/s is the Fermi velocity. The values of αand vF

were obtained from the LL spectra as discussed below. We note that the for Vg >

−10V the gate dependence of ED is significantly slower, indicating that most of the

gate induced charge is taken up by the MoS2 substrate. Indeed from the finite field

data we find that in this regime only ~25% of the gate induced charge goes the

graphene layer, the rest being absorbed by the MoS2 substrate. This suggest that EF

has entered the conduction band (CB) of MoS2 21

at which point the gate induced shift

in the position of ED is determined by the LDOS of the combined graphene/MoS2

system, as illustrated in the inset of Figure 2(b). Since the LDOS in the CB of MoS2 is

larger than that of graphene most of the charge is absorbed by the former. For

comparison we show in Figure 2(b) the gate dependence of ED for graphene deposited

on chlorinated SiO2 which remains insulating for all values of the applied Vg. In this

case the gate induced charge populates only states in graphene resulting in the

expected square-root gate dependence of ED for the entire range of applied Vg. For the

chlorinated SiO2 substrate we find α≈ 7.3 × 1010

cm-2

V-1

, V0 ~ 12V and vF

=1.1 2×106 m/s .

In the presence of a perpendicular magnetic field the dI/dV spectrum breaks up

into a sequence of LL peaks. The evolution of the LLs with magnetic field for

graphene on MoS2 and on chlorinated SiO2 at Vg = 10V is shown in Figures 3(a) and

3(b). In both cases the LL sequence follows the field and level index (N) dependence

characteristic of massless Dirac fermions as expected for single-layer graphene 2:

( )√ | | (1)

Here e is the magnitude of the electron charge and N > 0 (N < 0) corresponds to

electron (hole) levels. Fitting the measured sequence of energy levels to this

expression we obtain vF =1.21 0.02 ×106 m/s and vF =1.1 0.02 ×10

6 m/s for

graphene on MoS2 and chlorinated SiO2 respectively. One of the prerequisites for

observing well developed LLs is for the random potential to be smooth on the length

scale of the cyclotron orbit, ( ) √

√ . Therefore the field at which LLs

become resolved signals that the cyclotron orbit is sufficiently small to “fit” within

the characteristic puddle size of a particular sample37

. For graphene on MoS2, Figure

3(a), the LLs are already well resolved at 2T indicating that the characteristic puddle

size exceeds ( ) . For the case of graphene on chlorinated SiO2, Figure

3(a), LLs become distinguishable at 6T, indicating smaller puddles bounded by

( ) . The electron-hole puddles can be directly imaged through dI/dV

maps representing the spatial dependence the local doping. Figures 3(c) and (d) show

the maps of the N = 1 LL energy at 10T for graphene on the MoS2 and chlorinated

SiO2 substrates respectively. The spatial fluctuations in the map reflect local substrate

induced hole (blue) doping for negative energy shifts and electron (red) doping for

positive energy shifts. For the MoS2 substrate the average puddle size obtained from

the color maps ~ 30nm, slightly larger than the values reported for graphene on hBN

22, suggests that LL would remain well resolved down to magnetic fields of 0.5T. The

average puddle size for the chlorinated SiO2 substrate, ~10nm, is in good agreement

with that obtained from the LL spectra.

To study the effect of doping on the LLs we measured the gate dependence of

the dI/dV spectra at fixed field. The results for B = 8T and 10T (Supplementary

material S2) are summarized in the map shown in Fig4(a). Each vertical line

corresponds to the spectrum taken at a particular gate voltage. The pronounced

staircase features reflect the high degeneracy of the LLs each of which can

accommodate a carrier density of

= 10

11B[T] states/cm

2, where = 4.14 x

10-11

Tcm2, is the fundamental unit of flux. In the process of gating, each LL pins the

Fermi energy as it is filled causing the plateau features. The width of a plateau, Vg=

D/, reflects the gate voltage required to supply D carriers per unit area to the

graphene layer. The bias-voltage dependent shifts in the step position appearing as

diagonal lines on the map are due to tip induced gating.

For the data in Fig 4(a) in the regime where the MoS2 substrate is insulating, Vg

< −10V, we find Vg = 11.8V which gives 6.6 × 1010

cm-2

V-1

. For Vg > −10V,

the plateaus become much wider with Vg ~ 50V and 1.5 × 1010

cm-2

V-1

indicating that EF has entered the CB of MoS2. At this point ~75% of the carriers

introduced by the gate are taken up by the MoS2 substrate which can now provide

better screening of the random potential (Supplementary material S2).

In Figure4(b) we present the LL spectra for several values of Vg. Fitting in

Figure 4(c) the energies of the LLs obtained from these spectra with Eq. (1), we find

vF ~ (1.21 0.5) ×106 m/s. Furthermore, as shown in the inset, we find no systematic

gate dependence of vF. Since vF, is inversely proportional to the dielectric constant41

this implies that, in spite of the increased screening accompanying the entry of EF into

the conduction band, the dielectric constant of MoS2 does not depend on doping for

the range of Vg employed here, consistent with recent theoretical work42

. This value

of vF is comparable to that obtained on the chlorinated SiO2 substrate whose dielectric

constant ~4 is close to that of MoS2.

To illustrate the effect of screening we compare in Figure 4(d) the linewidth, E,

of the N=0 LL in the unscreened (Vg = 30V) and screened regimes (Vg = +25V).

Using a Gaussian fit we find E ~ 54mV for the unscreened case, which corresponds

to a quasiparticle lifetime of E/ = 12fs and to a scattering length of lmfp~

vFnm. In the screened regime we find a much narrower linewidth, E ~ 28mV,

indicating a significant reduction in scattering with correspondingly longer

quasiparticle lifetimes ~23fs and a mean free path of lmfp ~ 28nm. Interestingly the

mean free path obtained from the N=0 LL linewidth is comparable to the average

puddle size, in Figure 3(c), indicating that the electron-hole puddles are the main

scattering source in graphene. A similar analysis of the N=0 LL on chlorinated SiO2

(Figure 3b) gives a quasiparticle lifetime of ~ 10fs and lmfp~ 11nm comparable to

the puddle sizes in this system, so that here too electron-hole puddles are the main

source of scattering.

In summary, the quality of MoS2 substrates as measured by the quasiparticle

mean free path is remarkably good: in the unscreened regime it is comparable to that

in the best insulating substrates, hBN and chlorinated SiO2, while in the screened

regime it is larger still. The results presented here demonstrate that MoS2 substrates

are perfectly suited for accessing the low energy electronic properties of graphene

while at the same time providing great flexibility through controllable carrier densities

and tunable screening.

Acknowledgements

Funding was provided by DOE-FG02-99ER45742 (E.Y.A, G.L) , NSF DMR

1207108 (E.Y.A. , C.P.L) and National Science Council of Taiwan (C.P.L)

Figure 1. (a) Schematic of graphene on multilayer MoS2 substrate with gating

capabilities. The sample bias Vb is applied between the STM tip and the sample

contacted by a Ti/Au electrode. The edge of the graphene flake is marked by the

dashed line. The back gate voltage Vg is applied between the Si substrate and the top

electrode. (b)(c) Constant current STM topography image of graphene on MoS2 and

on chlorinated SiO2 respectively. The area of both images is (80nm×80nm) (d)(e)

Constant current STM topography image of graphene on BN(80nm × 80nm) with and

without moire pattern, respectively. (f) Profile line of Section view through (b),(c),(d)

and (e) indicating the corrugation of graphene on MoS2 (black), graphene on SiO2 (red)

and graphene on BN(blue) and graphene on BN with moire pattern(green). The

tunneling conditions were: Iset=20pA and Vb=0.4V. The Insets in (b-d) represent

zoom-in images to atomic resolution with scale bar of 0.3nm.

.

Figure 2. (a) dI/dV measurements of graphene on MoS2 taken at the same position for

different gate voltages. Curves are vertically displaced for clarity. Arrows indicate the

position of the Dirac point as discussed in the text. Measurement parameters: set point

current I = 20pA at Vb = 0.35V, AC modulation 5mVrms. (b) The Dirac point as

function of gate voltage for graphene on MoS2 (blue squares) and graphene on SiO2

(red squares). The solid lines represent the simulated gate dependence of the Dirac

point in the regime where the substrate is insulating. The top inset represents the

density of states of graphene on an insulating substrate. The bottom inset shows the

combined density of states of graphene (red) and the MoS2 substrate (teal) together

with the resulting gate dependence of the Dirac point energy as described in the text.

Figure 3. Magnetic field dependence of STS dI/dV spectra. (a),(b) Landau level

spectra for several magnetic fields and Vg= 10V for graphene on MoS2 and on SiO2,

respectively. The LL indices N = 0, ± 1, ±2..... are marked. STS parameters: set point

I=20 pA, Vb=0.35V, AC modulation 2mVrms. The lower panels are histogram of the

height distribution measured by AFM of MoS2, graphene on MoS2, SiO2 and

graphene on SiO2 as marked. (c),(d) Spatial variation of the N= 1 LL peak position

in B=10T obtained from a dI/dV map at Vg =0V representing the doping

inhomogeneity in graphene. STS parameters: set point I= 20pA, Vb= 0.35V, AC

modulation 2mVrms

Figure 4. (a) Gate map of the dI/dV spectra at 8 T. Each vertical line in the map

corresponds to a LL spectrum at a particular gate voltage. White stripes correspond to

the LL peaks energies as indicated by N = 0, ± 1, ±2.... STS parameters: set point

current I= 20 pA, Vb=0.4V, AC modulation 5mVrms. (b) LLs at Vg= 28V, 14V,

20V and 12V. (v) Solid dots are data points and the line represents a fitting for LLs of

graphene on MoS2 in B= 8T at Vg= 28V, 14V, 20V and 12V. Inset: Gate

dependence of Fermi velocity at Vg = 30~25V.(d) The Solid squares are data points

and the line represents a fitting for LLs N=0 with Gaussian at Vg=30V and 25V.

The curves are offset for clarity.

References:

1. Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos,

S. V.; Grigorieva, I. V.; Firosov, A. A. Science 2004, 306, 666.

2. Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K.

Reviews of Modern Physics 2009, 81, (1), 109.

3. Kotov, V. N.; Uchoa, B.; Pereira, V. M.; Guinea, F.; Castro Neto, A. H. Reviews

of Modern Physics 2012, 84, (3), 1067-1125.

4. Li, G.; Andrei, E. Y. Nat. Phys. 2007, 3, (9), 623-627.

5. Li, G.; Luican, A.; Andrei, E. Y. Physical Review Letters 2009, 102, (17),

176804.

6. Luican, A.; Li, G.; Andrei, E. Y. Solid State Communications 2009, 149, (27-28),

1151-1156.

7. Andrei, E. Y.; Li, G.; Du, X. Reports on Progress in Physics 2012, 75 056501

8. Neugebauer, P.; Orlita, M.; Faugeras, C.; Barra, A. L.; Potemski, M. Physical

Review Letters 2009, 103, (13), 136403.

9. Ishigami, M.; Chen, J. H.; Cullen, W. G.; Fuhrer, M. S.; Williams, E. D. Nano

Letters 2007, 7, (6), 1643-1648.

10. Stolyarova, E.; Rim, K. T.; Ryu, S.; Maultzsch, J.; Kim, P.; Brus, L. E.; Heinz, T.

F.; Hybertsen, M. S.; Flynn, G. W. Proceedings of the National Academy of Sciences

2007, 104, (22), 9209-9212.

11. Katsnelson, M. I. G., A. K. Phil. Trans. R. Soc. A 2008, 366, 195-204.

12. Ando, T. Journal of the Physical Society of Japan 2006, 75, (7), 074716.

13. Nomura, K.; MacDonald, A. H. Physical Review Letters 2007, 98, (7), 076602.

14. Hwang, E. H.; Adam, S.; Das Sarma, S. Physical Review Letters 2007, 98, (18),

186806.

15. Fratini, S.; Guinea, F. Physical Review B 2008, 77, (19), 195415.

16. Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Physical Review B 2006, 74, (23),

235443.

17. Martin, J.; Akerman, N.; Ulbricht, G.; Lohmann, T.; Smet, J. H.; von Klitzing, K.;

Yacoby, A. Nature Physics 2008, 4, 144.

18. Lui, C. H.; Liu, L.; Mak, K. F.; Flynn, G. W.; Heinz, T. F. Nature 2009, 462,

(7271), 339-341.

19. Dean, C. R.; Young, A. F.; MericI; LeeC; WangL; SorgenfreiS; WatanabeK;

TaniguchiT; KimP; Shepard, K. L.; HoneJ. Nat Nano 2010, 5, (10), 722-726.

20. Xue, J.; Sanchez-Yamagishi, J.; Bulmash, D.; Jacquod, P.; Deshpande, A.;

Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; LeRoy, B. J. Nat Mater 2011, 10, (4),

282-285.

21. Régis Decker , Y. W., Victor W. Brar , William Regan , Hsin-Zon Tsai , Qiong

Wu , William Gannett , Alex Zettl , & Michae F. Crommie. Nano Lett. 2011, 11,

2291-2295.

22. Chae, J.; Jung, S.; Young, A. F.; Dean, C. R.; Wang, L.; Gao, Y.; Watanabe, K.;

Taniguchi, T.; Hone, J.; Shepard, K. L.; Kim, P.; Zhitenev, N. B.; Stroscio, J. A.

Physical Review Letters 2012, 109, (11), 116802.

23. Li, G.; Luican, A.; Lopes dos Santos, J. M. B.; Castro Neto, A. H.; Reina, A.;

Kong, J.; Andrei, E. Y. Nat Phys 2009, 6, (2), 109-113.

24. Luican, A.; Li, G.; Reina, A.; Kong, J.; Nair, R. R.; Novoselov, K. S.; Geim, A.

K.; Andrei, E. Y. Physical Review Letters 2011, 106, (12), 126802.

25. Giovannetti, G.; Khomyakov, P. A.; Brocks, G.; Kelly, P. J.; van den Brink, J.

Physical Review B 2007, 76, (7), 073103.

26. Park, C.-H.; Yang, L.; Son, Y.-W.; Cohen, M. L.; Louie, S. G. Physical Review

Letters 2008, 101, (12), 126804.

27. Yankowitz, M.; Xue, J.; Cormode, D.; Sanchez-Yamagishi, J. D.; Watanabe, K.;

Taniguchi, T.; Jarillo-Herrero, P.; Jacquod, P.; LeRoy, B. J. Nat Phys 2012, 8, (5),

382-386.

28. Ponomarenko, L. A.; Gorbachev, R. V.; Yu, G. L.; Elias, D. C.; Jalil, R.; Patel, A.

A.; Mishchenko, A.; Mayorov, A. S.; Woods, C. R.; Wallbank, J. R.;

Mucha-Kruczynski, M.; Piot, B. A.; Potemski, M.; Grigorieva, I. V.; Novoselov, K. S.;

Guinea, F.; Fal/'ko, V. I.; Geim, A. K. Nature 2013, 497, (7451), 594-597.

29. Dean, C. R.; Wang, L.; Maher, P.; Forsythe, C.; Ghahari, F.; Gao, Y.; Katoch, J.;

Ishigami, M.; Moon, P.; Koshino, M.; Taniguchi, T.; Watanabe, K.; Shepard, K. L.;

Hone, J.; Kim, P. Nature 2013, 497, (7451), 598-602.

30. Hunt, B.; Sanchez-Yamagishi, J. D.; Young, A. F.; Yankowitz, M.; LeRoy, B. J.;

Watanabe, K.; Taniguchi, T.; Moon, P.; Koshino, M.; Jarillo-Herrero, P.; Ashoori, R.

C. Science 2013, 340, (6139), 1427-1430.

31. Kam, K. K.; Parkinson, B. A. J. Phys. Chem. 1982, 86, 463-467.

32. Andrea Splendiani, Liang Sun, Yuanbo Zhang, Tianshu Li, Jonghwan Kim,

Chi-Yung Chim, Giulia Galli and Feng Wang. Phys. Rev. Lett. 2010, 105, 136805.

33. Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Nature

nanotechnology 2011, 6, 147-150.

34. Han Wang, Lili Yu, Yi-Hsien Lee, Yumeng Shi, Allen Hsu, Matthew L. Chin,

Lain-Jong Li, Madan Dubey, Jing Kong ; Palacios, T. Nano letters 2012, 12

4674-4680.

35. Zongyou Yin, Hai Li, Hong Li, Lin Jiang, Yumeng Shi, Yinghui Sun, Gang Lu,

Qing Zhang, Xiaodong Chen, and Hua Zhang ACS Nano 2012, 1, 74-80.

36. Castellanos-Gomez, A.; Cappelluti, E.; Roldán, R.; Agraït, N.; Guinea, F.;

Rubio-Bollinger, G. Advanced Materials 2013, 25, (6), 899-903.

37. Luican, A.; Li, G.; Andrei, E. Y. Phys. Rev. B 2011, 83, 041405(R).

38. Li, G.; Luican, A.; Andrei, E. Y. Rev. Sci. Instrum. 2011, 82, 073501.

39. Tersoff, J.; Hamann, D. R. Physical Review B 1985, 31, (2), 805-813.

40. Zhang, Y.; Brar, V. W.; Wang, F.; Girit, C.; Yayon, Y.; Panlasigui, M.; Zettl, A.;

Crommie, M. F. Nat Phys 2008, 4, (8), 627-630.

41. González, J.; Guinea, F.; Vozmediano, M. A. H. Nuclear Physics B 1994, 424,

(3), 595-618.

42. Elton, J. G. S.; Efthimios, K. ACS Nano 2013, 12.